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Copyright © 2014 jsd

Ohm’s Law

*John Denker
*

Ohm’s law is commonly written

| (1) |

where it is understood that V is the voltage *drop* across the
resistor. That is, if we travel along the circuit in the direction of
positive conventional current I, then the voltage on the downstream
end of the resistor is lower than the voltage on the upstream end.

Note that if I move from a lower elevation to a higher elevation, the Δh is positive, according to the long-established conventional meaning of “Δ”.

Therefore it is not entirely logical to write Ohm’s law as

| (2) |

even though this is extremely common. Either there is a minus sign missing from equation 2, or they are using an exceedingly misleading idosyncratic definition of “Δ”, or they are going around the circuit backwards, contrary to the direction of positive conventional current.

It is smarter to write the voltage drop in the form

| (3) |

or even more explicitly as

| (4) |

where V_{1} is the upstream voltage and V_{2} is the downstream voltage.

Note that sticking absolute value bars into Ohm’s law is not an acceptable way to fix the problem. That’s because the equations with absolute value bars in them represent relationships that are wildly different from Ohm’s law. This should be obvious from the following figures.

Ohm’s Law

Not Ohm’s Law

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Copyright © 2014 jsd